The anisotropy of the water diffusion tensor inside brain causes contrast in diffusion images, which depends on the relative orientation of the diffusion gradients and the subject. Because the trace of a tensor is invariant upon rotation, measurement of this trace can reduce the orientation effect. A family of imaging pulse sequences is presented in which the signal intensity is weighted by the trace of the diffusion tensor in a single scan. The methods are demonstrated for chicken gizzard in several orientations with respect to the gradient frame of reference, and for ischemic injury in cat brain after middle cerebral artery occlusion. The sensitivity of the techniques to the presence of background gradients is measured and discussed in detail. As a result, pulse sequences are suggested that provide reliable diffusion constants in both homogeneous and inhomogeneous magnetic fields. The efficiency of the techniques for clinical application is also evaluated.